WO2002085045A1 - Procede et dispositif de calcul du prix d'utilisation d'une liaison specifique d'un reseau - Google Patents

Procede et dispositif de calcul du prix d'utilisation d'une liaison specifique d'un reseau Download PDF

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Publication number
WO2002085045A1
WO2002085045A1 PCT/IB2002/001187 IB0201187W WO02085045A1 WO 2002085045 A1 WO2002085045 A1 WO 2002085045A1 IB 0201187 W IB0201187 W IB 0201187W WO 02085045 A1 WO02085045 A1 WO 02085045A1
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price
link
network
change
demand
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PCT/IB2002/001187
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English (en)
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Georgios Cheliotis
Christopher M. Kenyon
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International Business Machines Corporation
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Priority to KR1020037013690A priority Critical patent/KR100634176B1/ko
Priority to EP02718461A priority patent/EP1380178B1/fr
Priority to AT02718461T priority patent/ATE480958T1/de
Priority to CA002443704A priority patent/CA2443704A1/fr
Priority to DE60237591T priority patent/DE60237591D1/de
Priority to US10/475,185 priority patent/US7742960B2/en
Priority to JP2002582640A priority patent/JP2004538550A/ja
Priority to AU2002249518A priority patent/AU2002249518B2/en
Publication of WO2002085045A1 publication Critical patent/WO2002085045A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G06Q30/02—Marketing; Price estimation or determination; Fundraising
    • G06Q30/0283—Price estimation or determination
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G06Q30/04—Billing or invoicing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/12—Accounting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L12/00—Data switching networks
    • H04L12/02—Details
    • H04L12/14—Charging, metering or billing arrangements for data wireline or wireless communications
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04Q—SELECTING
    • H04Q3/00—Selecting arrangements
    • H04Q3/0016—Arrangements providing connection between exchanges
    • H04Q3/0062—Provisions for network management
    • H04Q3/0066—Bandwidth allocation or management
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L12/00—Data switching networks
    • H04L12/54—Store-and-forward switching systems 
    • H04L12/56—Packet switching systems
    • H04L12/5601—Transfer mode dependent, e.g. ATM
    • H04L2012/5638—Services, e.g. multimedia, GOS, QOS
    • H04L2012/5639—Tariffs or charging

Definitions

  • the invention relates to a method and a device for calculating a price for using a specific link in a network.
  • it relates to a method and device making a decision based on the calculated price.
  • Bandwidth is becoming commoditized and markets are starting to appear. Potential behaviors of these markets are not understood because these markets are still in the early stages of development. This is reflected in the lack of current research on the structure and dynamics of network commodity market prices. A method is presented for constructing telecom commodity spot price processes. Bandwidth, like electricity, is not storable, so inspiration is drawn from electricity prices and models. However, unique network features of telecommunications require specific inclusion. These are: geographical substitution, referred to as arbitrage; quality of service (QoS); and the continuing pace of technological development. Developing liquidity acts as a further complication. Liquidity refers to the ease with which partners for trades at a given price can be found.
  • Price spikes are particular features of electricity prices and some modelling has been done there as described in "Stochastic models of energy commodity prices and their applications: mean-reversion with jumps and spikes", S. Deng, 1998. PSERC working paper 98-28, readable at http://www.pserc.wisc.edu/.
  • the method can be used to model for the expected telecom commodity price dynamics using a link-price process together with link-price modifications due to network effects.
  • a method is provided in which link-price changes are calculated based on a price difference, the link-price changes are combined over the network and the result is merged with market-induced price changes in order to calculate the subsequent occurring price.
  • a method wherein a decision whether to increase, decrease or maintain a transport capacity demand, the action of changing the demand accordingly, selling, buying or holding transportation bandwidth or the network or a sub-network thereof is performed.
  • This method has the advantage that the price calculation takes into account link-price changes that occur on a link independent from other links and also link-price changes that occur in dependence on the other links in the same network.
  • the market-induced price change is modeled to comprise one or more functions of a Brownian price-change, a Levy price-change, an Ito price-change, a Poisson price-change, a semi-Markov price-change and/or is modeled to comprise a function for price-spikes and/or price-jumps, this provides a relatively precise picture of the true price development that occurs in real networks.
  • the change-calculation step may comprise a shift-calculation step for determining an amount of an existing transport capacity demand that is to be shifted from the specific link to the alternative path in response to the determined price difference, and an effect-calculation step for determining the link-price change effected by the determined transport capacity demand, that is to be shifted, on the link-price for using the specific link.
  • This mechanism of demand reacting on the price difference is a model that gives a simple but realistic picture of real-world network demand behavior. When the transport capacity demand is approximated with a linear function this provides a good simplification of the calculation mathematics which nevertheless is accurate enough to provide acceptable results. The same holds true for the modelling of a transport capacity supply as having a constant elasticity.
  • the amount of demand to be shifted from the specific link to the alternative path may be assumed positive, thereby taking into account the fact that the price difference situation is insofar asymmetric as a cheaper alternative path will redirect demand to this path but a more expensive alternative path will not necessarily lead to a corresponding demand shift from that alternative path to the path/link looked at.
  • a decision step for deciding in view of the calculated link-price, whether to increase, decrease or maintain the transport capacity demand for transporting a unit, preferably an information unit, over the specific link or the alternative path, is a practical and advantageous application of the calculation result because the calculation result will determine the price at which the demand can be satisfied, leading to a corresponding contract, which is naturally oriented to be closed as cheaply as possible for the demander.
  • the demander may hence in a demand-change-step increase or decrease the transport capacity demand for transporting the unit over the specific link or the alternative path in response to the calculated link-price.
  • Another advantageous application would be an action-step comprising one of a buy/hold/sell action for transportation bandwidth on the network in response to the calculated link-price, making the bandwidth a traded good, allowing to make profit from the determined price difference.
  • Yet another advantageous application would be an adaptation step wherein the transport capacity of the specific link or a different of the links in the network is changed in response to the calculated link-price, e.g. by changing transmission equipment, such as switches, cross-connects, repeaters, multiplexers, amplifiers, fibers, or settings thereof.
  • This provides a network which is adaptively operated in a manner responding to the calculated price.
  • the network capacity can thereby be improved, e.g. by increasing the network capacity in paths which are expensive, in order to attract demand.
  • the invention is directed to a method for calculating in a network that comprises links, a price for using a specific link in the network.
  • the method comprises the following steps:
  • a merging step for merging the determined total price-change with a market-induced price change in the price for using the specific link, to calculate the price for using the specific link, wherein the market-induced price change is being driven by at least one random variable.
  • Fig. 1 an example of a network with three nodes and three edges
  • Fig. 2a a graph depicting for an edge the relation between price p and quantity of demand q under the influence of a price change removing demand x from that edge
  • Fig. 2b a graph depicting for an edge the relation between price p and quantity of demand q under the influence of a price change moving demand x to that edge
  • Fig. 3 a network with two nodes connected via various paths under the influence of demand shifting
  • Fig. 4 a flow chart for the method of calculating a new price in a price-dynamic network according to figure 1.
  • Fig. 5a the arbitrage versus the side length ratio for 10% (lowest line), 50%, 100%, 150%, 200% (highest line) of short-term price volatility at 0% long-term price trend uncertainty
  • Fig. 5b the arbitrage versus the side length ratio for 0% (lowest line), 10%, 20%, 30%,
  • Fig. 5c the net present value for the arbitrage in fig. 5a
  • Fig. 5d the net present value for the arbitrage in fig. 5b
  • Fig. 6a the mean price change on a fixed-length link versus short-term volatility
  • Fig. 6c the standard deviation SD of the price change on a fixed-length link versus short-term volatility
  • Fig. 6d the standard deviation SD of the price change on a variable-length link versus short-term volatility.
  • Fig. 7d the change in the SD of the NPV versus the side length ratio
  • Fig. 8 a combined contract network topology for Asia, USA and Europe,
  • Fig. 9 frequency histograms of the triangle-side ratio-distribution for three different cases, using 10%-bins,
  • Fig. 10a forwards curves for DS3 capacity from New York to Los Angeles (NY-LA), the delivery month starting in February 2001 and going to January 2002, with a contract duration of one month.
  • NY-LA New York to Los Angeles
  • Fig. 10b forwards curves for DS3 capacity from New York to Los Angeles (NY-LA), the delivery month starting in February 2001 and going to January 2002, with a contract duration of one year at a monthly rate,
  • Fig. 11a the distribution of F(T,T) in three different network situations and without a network
  • Fig. l ib the option price versus the strike price for a call option on forward price with and without a network
  • Figure 12 the percentage difference of the call option prices in two network cases and an isolated-link case.
  • a network also referred to as graph G n , comprising a first node a, a second node b, and a third node c is depicted.
  • the first node a is connected to the second node b via a first link ab.
  • the first node a is connected to the third node c via a second link ac.
  • the third node c is connected to the second node b via a third link cb.
  • a first path FIi leads from the first node a to the second node b and comprises the first link ab.
  • a second or alternative path ⁇ 2 leads also from the first node a to the second node b.
  • This alternative path ⁇ 2 comprises the second link ac and the third link cb.
  • a corresponding price pab, Pac, p C b is valid at a certain point in time.
  • These prices pab, Pac, Pcb are the prices charged to a network user by a service provider, who may be the network owner or renter, for the service of providing at that point in time a specific amount of transport capacity on the corresponding link ab, ac, or cb for allowing transportation units over that link ab, ac, or cb.
  • the network can be any transportation network, such as a street network, a mail delivery network, or as exemplarily selected here, a communication network.
  • the units to be transported over the communication network are information units, e.g. data packets. A particular example could be data traffic over the Internet or a telecom network.
  • the bandwidth is a geographically distributed commodity and in real information networks the major long-distance suppliers form an oligopoly.
  • Geographical arbitrage This means that, given equivalent QoS, the cheapest of all available paths will set the end-to-end price in a competitive liquid market. This is due to the fact that the actual path is irrelevant with respect to information transport, as long as certain QoS requirements are met. The set of paths connecting two given geographical locations at the same QoS level are perfect substitutes.
  • Supply/demand disassociation This refers to the fact that the demanded product is not always the one supplied.
  • the demand In electricity markets, the demand is e.g. for power at one location but the power is usually supplied from another location. This has been a particular problem in some markets where power was available at one location but, for congestion or legal reasons, could not be transported to where it was needed.
  • bandwidth markets the demand is for an end-to-end service but the actual supply is made - at a physical level and an investment level - on a link-by-link basis. Collections of links may be owned by single entities, such that for subsets of the whole network the investment policy will have some coherence. Also new links can be created, but the disassociation remains.
  • Network effect is the argument of increasing economies-of-scale, which means that the utility of a service grows with the number of people - or devices - that are attached. In general the utility grows with some power of the number of users, not simply linearly.
  • Non-storability Inventories act to smooth variations in supply and demand. When no inventories exist, prices can jump if supply or demand changes suddenly. Prices can also change suddenly when the perception or expectation of the supply- or demand status suddenly changes. Bandwidth is non-storable, so price jumps and spikes can occur. Non-storability is a determining factor in electricity price modelling. Jumps and especially spikes are observed due to weather events sometimes in combination with equipment failures. In fact, even in commodities where storage is possible, like oil, large-scale political events can cause jumps and spikes in the price.
  • Liquidity Currently the bandwidth market is less liquid than the electricity market or many other commodity markets. Trading-volumes are picking up and ongoing deregulation of the industry along with universal trading contracts will assist in reaching higher levels of liquidity. In any case, not all traded locations are expected to be equally liquid in the future.
  • Demand inelasticity Provided that most consumers do not react on the time-scale of market trading and settlement, demand inelasticity will be a feature of total point-to-point demand on that time-scale.
  • demand will be elastic thanks to automation technologies, such as software agents, electronic auctions and least-cost routing which allow for fast switching between substitutes, i.e. alternative paths.
  • This elasticity will exploit market liquidity and also contribute to it.
  • Inelastic demand is a current feature of short term electricity markets. In the assumption of inelastic point-to-point demand, some care should be given to network effects which involve only demand-shifting between substitutes, and not changes in total demand. This is why in the analysis that follows it is assumed that point-to-point demand is conserved, whereas generally demand for a particular substitute is fairly inelastic but not necessarily completely inelastic.
  • Deregulation In the bandwidth market a transition is going from mostly closed proprietary networks towards interoperable networks.
  • the interoperability takes the form of a common infrastructure layer, e.g. IP, open public points of interconnection and universal trading contracts (UTC) with QoS guarantees.
  • IP common infrastructure layer
  • UTC universal trading contracts
  • These UTCs will have effects that mirror those from deregulation in the conventional utilities markets.
  • deregulation has appeared over a period of years and in a highly heterogeneous fashion. This development can be expected to also appear in bandwidth markets. However instead of geographically restricted patches there will be increasingly linked interconnection points.
  • bandwidth development A dominant factor is bandwidth development. There are two related areas: bandwidth and switching/routers. Bandwidth increases with both the increase in packing down a single wavelength and also with the increase in the number of wavelengths that can go down a single fiber, e.g. using Dense Wavelength Division Multiplexing, DWDM. Since switches are inherently parallel devices they also exhibit this combination of improvements: They improve as chips improve, and they improve with packing multiple switching units. There is also an expected transition to all-optical wavelength-switching within the next 5 to 10 years. The combined effect of technological development and competition leads to a continuous drop in the cost of transporting a Megabit per second per mile.
  • Capacity expansion It takes a relatively long time to build a new fiber network and many months to put a new long-distance conduit in place. However, once the conduit is in place new fibers can be added relatively quickly. Also, conduits can house dark fibers, i.e. cables without the equipment that is necessary for transmission. In addition, with multimode fibers and DWDM, more wavelengths can be added to those already present in a lit fiber. If new equipment is required, this depends on manufacturers schedules. Thus, different amounts of capacity can be added over a range of time-scales. This is different from electricity where the shortest time-scale for adding significant new capacity is a year.
  • Suppliers of bandwidth may have significant flexibility in assigning network resources for the fulfillment of different end-to-end contracts. This is due to routing- and bandwidth management tools which allow for a number of different allocations, depending on the type of contracts the supplier wishes to offer. The amount of flexibility depends on the design of the underlying network. Generally, a network with more switching points will provide more flexibility at the expense of QoS, because more contention/failure points are added. In a similar manner, a power plant's resources can be assigned to different markets, but the allocation problem is different since it occurs only at one place, namely the plant, not on the distribution network.
  • a contract C is an agreement between a supplier and a buyer, whereby the buyer agrees to pay a specific price p and the supplier agrees to in exchange supply a specific network capacity to the buyer.
  • the price development is such that observed prices, i.e. a market-observed outcome, C ⁇ may contain arbitrage opportunities.
  • Market forces act both to remove the existence of arbitrage and to disturb the link-prices via normal and unusual information and changes in supply and demand. These two processes in general combine to produce the next set of observed link-prices.
  • the arbitrage removal occurs relative to the observed state of contract prices. However, other market forces are still acting and this occurs at the same time. Thus the new state may not be arbitrage-free, even with a high liquidity, because there is always the potential for new arbitrage opportunities to be created.
  • geographical arbitrage removal and market-induced price changes can be modeled separately or in combination. For simplicity, they will first be described separately and then a combined formulation will be given.
  • the links ab, ac, cb can be defined as indivisible contracts C offered between pooling points, also referred to as the nodes a, b, c.
  • pooling points also referred to as the nodes a, b, c.
  • Any party may combine the link contracts C to form end-to-end contracts.
  • any party buying such an end-to-end contract may be able to split it according to the pooling points, i.e. nodes, along the path II to create new link or multi-link contracts.
  • the prices p between any pair of nodes a, b, c may be observed on the market, but these are formed from the link-prices.
  • Multi-link-price processes are here not modeled directly.
  • Link-price development is modeled as a combination of three factors: link-price changes, geographical arbitrage, and liquidity. If the market is completely illiquid then if a geographical-arbitrage opportunity appears, there will be no action by the market participants affecting the link-prices p to move the market in a direction to remove the opportunity. This means, traffic, being the flow of transportable good following a contract C, will not take the cheapest available path P if the market is illiquid. On the other hand in a completely competitive, i.e. liquid, market, arbitrage opportunities will only last at most until the next trade occurs. Liquidity is hence the factor that describes the ability of the market to react e.g. with a demand shift to a price shift. The more liquid the market is, the quicker a price shift is followed by a demand shift, adapting the demand distribution to the price shift.
  • the subsequently described independent-link-price process models for the example of the first link ab the evolution of the link-price p ab on this link ab as if it were isolated. It hence describes the market-induced development of the link-price p ab . Different forms of dependence can be introduced.
  • the realized link-price p a b in the market for the first link ab is formed from this link-price-calculating process together with geographical arbitrage arguments and liquidity considerations.
  • the independent-link-price process represents, as far as possible, the evolution of supply of and demand for link capacity that providers make available in the form of indivisible contracts between the nodes a, b. First, the generating equations will be described and then their rationale. Independent Link Price
  • the link-price p is modeled for each link ab, cb, ac based on an Orstein-Uhlenbeck process with the addition of a process for long-term mean, spike- and jump terms. Limited regime-switching, induced by spike terms on the effective mean, are also incorporated. This process can be termed as a Shock-Regime-Reverting process or SRR process. The hypothesis is made that if there were no network around the single link then the link-price p would develop as follows:
  • U is a two state ⁇ 0, 1 ⁇ semi-Markov process, wherein an identification is made between the states and the numbers zero and unity, with corresponding rate parameters ⁇ u, ⁇ _-
  • T stands for a Gamma distribution with a scale parameter g and a shape parameter ⁇ .
  • T stands for a Gamma distribution with a scale parameter g and a shape parameter ⁇ .
  • the distribution T (g, ⁇ ) has a mean g ⁇ and a variance g 2 ⁇ .
  • the semi-Markov process U jumps from state ⁇ 0 ⁇ to state ⁇ 1 ⁇ then the logarithmic link-price X increases by G and the mean g ⁇ to which the process U is reverting also increases by G.
  • logarithmic link-price X decreases by the same amount that it previously increased by and the corresponding extra term in the mean g ⁇ is dropped.
  • a link-price spike is created.
  • the link-price p will stay in its current state for an exponentially distributed amount of time as given by the rate parameters ⁇ U; ⁇ _-
  • V is a Poisson process with a corresponding Poisson rate parameter ⁇ v and
  • jump down 1 J Jumps may be equally probable in both directions or not as determined by the probability of an up-jump. These jumps act additively on the logarithm of the link-price p and hence represent a multiplication of the current link-price p.
  • ⁇ is the speed of link-price reversion to the average link-price X ; ⁇ is the scale of a driving Brownian motion dW of short-term link-price change increments; v is the (positive) instantaneous rate of average link-price decrease and there is an uncertainty p about this rate which is also referred to as exponential improvement v.
  • X log p, log-normal changes in the link-price p are hypothesized.
  • dZ is a Brownian motion of long-term link-price change increments uncorrelated with the short-term link-price change increments.
  • X is called here an average link-price because it is the value towards which the link-price p reverts. It is not an arithmetic average. Since there is no storage there is no requirement that the process be a Martingale under any particular risk-neutral measure.
  • the link-price process model is hereinafter described in more detail. Since the process is a semi-Markov jump diffusion with regime-switching, the present determines the future. It is assumed that ordinary market news move the link-price continuously and are responsible for the driving Brownian motion dW of short-term link-price change increments.
  • the long-run mean X logarithmic in price-terms, is expected to mimic the technological development of communication capacity with its exponential improvement v.
  • the degree of the exponential improvement v is not known, but an estimate may be used therefor.
  • single-mode fiber capacity has shown exponential growth
  • multimode transmission e.g. DWDM
  • Other such disruptive improvements are possible, e.g. long-distance transmission with no repeaters, all-optical switching, etc.
  • This uncertainty is modeled with the scale p of the driving Brownian motion dZ of long-term link-price change increments. These factors represent random variables which drive the market induced price change dX.
  • Spikes in link-prices can be observed in electricity prices and are the result of demand being very close to available supply followed by e.g. some equipment failure. Congestion can be observed on telecom networks, as well as equipment failures leading to outages. Thus, spikes are also included as a feature in the link-price process.
  • a spike is defined as a sudden increase in link-price followed quickly by a similar decrease in link-price.
  • the mean for reversion is altered to include the magnitude of the spike. This change in regime is reversed when the spike ends.
  • Spike sizes are modeled exemplarily with a Gamma distribution and generate reversible step changes in the link-price p.
  • Jumps are observed in oil prices. Given that the owners of long-distance networks also form an oligopoly there is a potential for link-price jumps. These jumps may be local to a single link or more general. Jump occurrences are modeled here with a Poisson process with a given rate that describes how many jumps are expected per unit time. These jumps may be positive or negative and again are modeled with Gamma distributions.
  • a form of dependence between different link-prices can be modeled by introducing correlations in the driving Brownian motion dZ for the long-term variation and the driving Brownian motion dW for the short-term link-price variation, between different links.
  • a more network-specific form of dependence, namely geographical arbitrage, is however examined here.
  • the introduction of a correlation structure across a node allows to model the introduction of a node on a previously undivided path. If the new node is actually redundant and all demand and supply actually crosses it, perfect correlations can be used in the driving processes on both sides of it. This does still permit separation of rare events on either side of the node.
  • Geographical arbitrage is the term that is used to describe the existence of at least two different end-to-end link-prices between two nodes that are joined by a single link at a given end-to-end QoS. These two end-to-end link-prices may each be formed from one or more links but will both provide a minimum specific QoS level. In a liquid market this situation will not persist when all other factors are equal.
  • Definition 1 A simple geographical arbitrage opportunity exists when multiple links can be substituted for a single link and when the total price of the substituted links is less than that of the single link. It is assumed that the QoS is equivalent between the single link and the end-to-end QoS of the substituting links, i.e. the links of the alternative path II 2 .
  • a link represents an indivisible contract. Not all contracts offered on the market may be indivisible in general. For that case the following specification of geographical arbitrage is given:
  • Definition 2 A geographical arbitrage opportunity exists when multiple contracts can be substituted for a single contract and when the total price of the substituted contracts is less than that of the single contract.
  • the QoS is assumed to be equivalent between the single contract and the end-to-end QoS of the substituting contracts.
  • Simple geographical arbitrage provides an immediate downward pressure on the link-price of a single link. How fast this pressure acts, depends on how easy the substitute path is to identify, and how liquid the market is.
  • a decrease in the link-price of a single link implies that some part of the total end-to-end demand has shifted from that link to a cheaper alternative path.
  • the increase in demand in the alternative path should result in a link-price increase on all links of that path.
  • the question arising here is how to quantify the effect of movement of demand from a link to an alternative path at the link-price level.
  • the competitive situation on single links will also be important. If there is only one provider, or if there is only one provider left with spare capacity, then there will also be upward pressure on the single-link-price when it is the cheapest path between its endpoints, i.e. nodes. This upward pressure will be limited by the elasticity of demand and by the price of the cheapest alternative path with an equivalent QoS.
  • the first link ab shall be defined a set ⁇ abq of all paths i, ⁇ 2 between the first node a and the second node b which provide at least a QoS q.
  • the set of prices p ⁇ ⁇ patty I k € ⁇ abq ⁇ , comprises the observed link-prices pate for ⁇ abq .
  • x describes how fast the no-arbitrage correction f(p ⁇ , ⁇ _bq), i.e. the development that serves to remove the arbitrage situation, takes effect.
  • the relaxation constant ⁇ is the quantification of the system liquidity.
  • the liquidity is the speed with which geographical arbitrage opportunities are removed, expressed via its time constant ⁇ . It can be derived from market observation results.
  • the no-arbitrage correction function f also embodies the speed and extent to which applications and electronic agents can re-balance the flow in the network G Mon on the time-scale of network link-price development.
  • the link-prices p on the alternative path ⁇ 2 will also be affected.
  • a correction on the direct link, labeled d here, from the observed price p d on that link d to the next price p d ' on the same link d has the effect of a left shift x of the demand curve for that link d, because on that link d the total population that creates the demand is reduced, and hence the percentage that creates a demand for a specific price.
  • the total end-to-end demand in the network G is assumable to be inelastic in the time-scale examined, which is short e.g. one day, so this same demand is directed to the alternative path ⁇ and added to the demand of each link ac, cb in that path ⁇ 2 , resulting in a shift of the corresponding demand curve to the right by the same amount x, as depicted in fig. 2b.
  • Fig. 3 shows an example of a different graph in which between the first node a and the second node b four different paths are present.
  • a demand shift (-x-y-z) on one path results here in a corresponding total demand shift on the other, alternative paths, in that one path receives a corresponding demand shift (x), another path receives a corresponding demand shift (y) and a third path receives a corresponding demand shift (z).
  • These shifted demands appear on all links belonging to the same path.
  • the demand elasticity E d is uniform across several links and can be estimated from real-world data. Since the time-scale is here relatively small and the elasticity E d of the demand q d is generally inversely proportional to the time-scale, values of E d > 2 are plausible including the case of completely inelastic demand q d where the elasticity E d goes to infinity.
  • the only relevant factor here is the speed at which the capacity supplied on a set of ports at a node location can be altered. This depends on the network management technology employed at the nodes and in the providers' networks. Given that the nodes will employ the same or similar technologies for bandwidth management and that the total supply on each link should be dominated by the same set of long-distance providers, the factor l s is assumed to be uniform across all links. The capacity offered at the nodes can be altered at the speed of bandwidth management operations (very fast) and the incremental cost of offering one extra unit of bandwidth in this time-scale is close to zero. Therefore the supply will be very elastic and bigger than l d .
  • a simple arbitrage case can be resolved by treating the demand q d as a network flow which is conserved point-to-point, i.e. node-to-node while being allowed to shift from the direct link d to an alternative path so as to achieve a load-balancing effect.
  • Xk is defined as the amount of network flow shifting from the direct link d to all links of the alternative path ke ⁇ / (a, b) ⁇ . If x k is permitted to be only positive this implies that a substitution of the alternative path for the direct link d is allowed, but not the alternative path II to act as substitute for another alternative path ⁇ . There may be no end-to-end flow on a substitute path ⁇ even though each link may have flow. Thus in general, end-to-end flow cannot move from a multi-link substitute path II to anywhere, which suggests this restriction. Then the no-arbitrage state for the direct link d and the alternative path k can be written as
  • ⁇ k is the arbitrage size, i.e. the absolute difference of proposed prices between the first node a and the second node b on one hand and the path k on the other hand.
  • the no-arbitrage state can be rewritten as follows:
  • arbitrageurs could take into account expected movements of the market as embodied in the expected value E [ ⁇ ( X+ GU - X)] in the size of their actions in dN.
  • E the expected value
  • the expectation E here would be with respect to the real measure since the underlying good is non-storable. This would become more important with low liquidity because then the time-scale of their actions would increase.
  • FIG 4 a block diagram for an algorithm for calculating the next price on the network G n , as depicted in fig. 1 is shown.
  • a comparison step II for determining a price difference between the price p for using the specific link ab, ac, cb and the price for using instead of the specific link ab, ac, cb an alternative path II in the network, which does not comprise the specific link, is performed.
  • the first link ab this means that it is checked whether p ab > p ac + p cb . If this is the case, this means that the alternative path ⁇ 2 is cheaper to use than the first path i.
  • a change-calculation step UI for determining a link-price change in the price p for using the specific link ab, ac, cb, and a link-price change in the price p for using the links in the alternative path fl 2 , in response to the determined price difference.
  • the equation [9] can be used.
  • ZabXab, z ac Xab, z cb x ab , z ab x ac , z ac x a c, z cb x ac , z ab x c b, z ac x c b, z cb x cb which is done in an effect-calculation step IV for determining the link-price change zx effected by the determined transport capacity demand q d , that is to be shifted, on the link-price p for using the specific link.
  • a combination step V for the specific link the determined link-price changes on the price for using the specific link from all links in the network G Titan are combined to determine a total price-change ⁇ dN ab for the specific link.
  • the terms z ab x ab , Za b Xac, z ab x cb are combined to a common term dN ab (VI).
  • VI common term dN ab
  • step VII for merging the determined total price-change ⁇ dN ab with a market-induced price change in the price p for using the specific link, to calculate the price p for using the specific link, wherein the market-induced price change is being driven by at least one random variable.
  • the market-induced price change is modeled as a combination of two different Brownian motions dW, dZ, a Poisson process dV and a semi-Markov process dU.
  • This market-induced price change is merged with the determined total price-change dN to define the logarithmic price change dX and eventually the new price p'.
  • the described algorithm hence incorporates a similar functionality as described in principle by the equation [7], namely a dependence of the new price p' on the previous price p on that link and on the other links, and on the liquidity of the underlying market, expressed by the liquidity term ⁇ .
  • the new price p' is the price that based upon the observed factors will follow the previous price p on the specific link.
  • This new price p' can be calculated for several of the links, forming a subnetwork of the network G n , or for the whole network G hosky itself. Since it is the natural desire of an entity using transportation facilities for business or private purposes to keep the incurring costs as low as possible, a change in the transfer price p influences the decision over which of several possible paths II to have the transport performed. If the price p is lower on an alternative path ⁇ the demand for transport capacity can be directed to the cheaper path Tl.
  • This step can of course be automated by giving the corresponding system the decision rule according to which the decision is taken.
  • This decision can influence only one unit, or also be applied to a stream of such units.
  • the decision-making unit can hence make a decision at any point in time, depending on the price development, or make its decisions only at predetermined moments.
  • a demand-change-step can be carried out in which the demand q d for transporting the unit over the specific link ab or the alternative path _1 2 is decreased or increased in response to the calculated link-price p. This step effects a demand-routing in accordance with the calculated price p.
  • the price development is not only of interest for network users but, as it is the case with stocks and stock options, may be of interest for entities who want to make a profit from the price differences. Therefore, the price calculation can also be used by those entities and be followed by an action-step comprising one of a buy/hold/sell action for transportation bandwidth on the network G n in response to the calculated link-price p.
  • the bandwidth, respectively transport capacity can hence be traded as a separate good.
  • the whole process described above can be executed several times sequentially to provide a link-price series comprising several of the subsequent calculated link-prices p.
  • This link-price series then consists of a row of prices that are to appear after each other.
  • This whole procedure can again be executed several times to provide several of the link-price series.
  • the different series can for instance be combined to obtain an average thereof.
  • a discounting step can first be carried out, wherein the link-prices p within the link-price series are discounted back to their present-value, thereby providing discounted price series, followed by an integration step wherein the discounted price series are integrated for the network Gemis or a sub-network thereof, for obtaining therefrom a network present-value for the network G n or a sub-network thereof.
  • the calculation result be it the single calculated price, the link-price series, or the network present-value, can be used as a decisive factor in a decision step comprising one of a buy/hold/sell action for the network G Tha or subnetwork.
  • Another possibility of use of the calculation result is the carrying out of an adaptation step wherein the transport capacity of the specific link or a different of the links in the network G n is changed in response to the calculated link-price p, e.g. by changing transmission equipment, such as switches, cross-connects, repeaters, multiplexers, amplifiers, fibers, or settings thereof.
  • This can be particularly done by using a network hardware that provides the functionality of allowing to change network-specific settings, like a controllable transfer capacity, damping, amplification or the like.
  • the QoS offered is set on each side to unity and the allowed QoS is set to two.
  • the QoS is set to two.
  • arbitrage opportunities only last for the time-step on which they are observed.
  • New geographical arbitrage opportunities may arise at each time-step but load-balancing, i.e. demand shifts, act to fully remove them on each subsequent time-step together with the usual price drivers embodied in the stochastic processes for the links.
  • the right upper panel (b) shows the arbitrage versus the side length ratio for 0% (lowest line), 10%, 20%, 30%, 40% (highest line) of long-term price trend uncertainty at 10% of short-term price volatility.
  • the lower right panel (d) shows the net present value for this arbitrage.
  • the NPV of arbitrage opportunities also increases with the volatility to almost 2.5% of the NPV of the total network G n . This is fact even with the considered highly liquid market. Long-term price-trend uncertainty - alone - is insignificant in creating valuable arbitrage opportunities less than 0.1% of the network NPV. This is probably because the scale of arbitrage opportunities, i.e. their value, is mostly determined by changes in the Brownian motion ⁇ dW and changes in the mean logarithmic link-price X are scaled down by the speed of the mean reversion ⁇ .
  • the geographical distance between the nodes i.e. the length of the respective links
  • the mean price on that link is proportional to the mean price on that link.
  • Figure 6 shows the percentage change in the mean spot price p after one year, here 252 trading days, and the standard deviation of the observed changes in prices after one year as a percentage of mean prices.
  • Fig. 6a shows the mean price change on a fixed-length link versus short-term volatility.
  • Fig. 6b shows the price change on a variable-length link versus short-term volatility.
  • Fig. 6c shows the standard deviation SD of the price change on a fixed-length link versus short-term volatility.
  • Fig. 6d shows the standard deviation SD of the price change on a variable-length link versus short-term volatility.
  • the numbers for the different lines, at the right side of the panels give the number n for the sides relation n: 10: 10, i.e. increasingly obtuse triangular networks.
  • the crossed line gives in comparison the case for an isolated link (iso).
  • the short side as depicted with the heavy dots in the right top panel of fig. 6, becomes longer and the longer sides, depicted with the heavy dots in the left top panel of fig. 6, become shorter.
  • the scale of these changes in the mean prices is very different.
  • the short side may increase in price by 250% rather than decreasing by the expected, i.e. baseline, case of around 5%; whereas the long side simply decreases in price by 30% rather than the expected case of around 5%.
  • the baseline case will always be the same for the two different sides because when they are isolated they behave exactly the same, apart from a constant term which drops out when percentage changes are considered.
  • 1: 10:10 the arbitrage effects push the triangle towards 2.5:7:7 after one year.
  • Figure 7 shows the effect of geographical arbitrage liquidity on the NPV of a triangular network. In its upper left panel (a) the relative NPV versus short-term volatility is depicted.
  • This NPV is the sum of the NPV for each edge of the triangle.
  • the baseline, isolated link, triangle NPV changes (increases) with increasing short-term volatility, as shown in the right top panel.
  • the difference between different networks with different triangle ratios is less significant than the change in NPV relative to zero volatility which is nearly 140% of the zero-volatility NPV.
  • the spread on triangle shape is less than 10%. There is even less difference for the triangle shape for the SD of the network NPV in terms of the mean NPV for the same short-term volatility.
  • the lower panels (c), (d) of figure 7 show the additional effect of geographical arbitrage on the network NPV.
  • a realistic international topology is used to analyze the applicability of the results. Specifically, the potential presence of triangles of link contracts and their side ratio distribution is quantified.
  • An edge or link is created between two nodes in the map if there is at least one backbone which could connect these nodes without crossing any other node. If all possible network-level paths would cross other node locations, the link between the nodes cannot be offered as an indivisible contract. An example of this is the connection between Dallas and London. All network paths would cross the New York or Washington DC nodes, Dallas-London is therefore not an edge in this graph. As a rough approximation of an edge's length the geographical distance between two locations is computed using the Haversine formula. This method will generally underestimate the actual length of a network connection.
  • Fig. 9 shows frequency histograms of the triangle-side ratio-distribution for these three cases, using 10%-bins. These ratios are constructed from geographical distance ratios, not observed prices. However, at least some network costs are roughly linear with distance and these will dominate the mean trend v for long-distance paths.
  • the black bars are triangles where two fixed-length sides are within 10% of the variable side, the grey bars are for 20%, the white bars for 30%.
  • a method for constructing in particular a telecom commodity spot price process that reflects its unique characteristics.
  • the commodity envisaged is point-to-point bandwidth between the nodes.
  • the prices for network links decrease on average to reflect a decreasing technology cost v.
  • Changes in the mean prices for the network links are altered by network effects (geographical arbitrage) and the difference increases with increasing short-term volatility.
  • the price-change could be in either direction depending on the triangle side ratio and on which side is being examined.
  • the volatility (standard deviation) of the observed prices is almost always reduced by network effects and this could be by up to half.
  • the total network present value NPV over one year sees a decrease of up to 10% with acute triangles and an increase of up to 3% for equilateral triangles due to the network effects.
  • the volatility of the network value shows a consistent decrease of up to 30% with the least decrease for mildly acute triangles (5: 10: 10).
  • the link-price processes are inspired by jump diffusions as they appear in oil and electricity markets.
  • the major difference is the explicit inclusion of geographical (no-)arbitrage terms that express the effects of the network topology on the price dynamics.
  • Short- and long-term dynamics with short- and long-term variations or alternatively a stochastic convenience yield are considered.
  • the mean drift of the long term dynamics are here taken explicitly negative.
  • the prices decrease on average due to technology development rather than they increase.
  • the other additional new factors relative to these sources are the addition of jump- and spike terms and especially regime-switching models.
  • Spikes are expected to be more important than price jumps. In oil markets price jumps are basically the result of changes in the status of OPEC and different states of this status may be prolonged.
  • the forward curve development is modeled explicitly and the spot price is just the shortest-term forward.
  • Forward-markets are expected to be larger and more active than spot markets, as is true for most commodities.
  • Another extension to this method is going into more depth on effects of rare events linked with QoS constraints.
  • the invention hence provides a method to model e.g. telecom commodity prices taking into account network effects inherent to bandwidth markets. These network effects produce highly significant changes in the price development and network value. These changes depend on the network topology for both, sign and magnitude. Comparison with a plausible future network topology show that extreme topologies, from a network-effect point of view, will be common.
  • a forward contract is a transaction between two individuals whereas a futures contract is an exchange-traded instrument. Both contracts are for the future delivery of an asset at a fixed price agreed upon at the start of the contract. Because exchanges usually have margin requirements adjusted daily to reduce default risk, futures and forwards have different sensitivities to daily interest rate fluctuations. As interest-rate modelling is here not an objective, a constant risk- free interest rate r is assumed. Thus forward and futures prices are the same, and the two terms are used interchangeably.
  • the bandwidth-trading market is represented by a contract graph G(N,L), where N are the nodes of the graph and L are the links between the nodes.
  • a link in the contract graph G(N,L) represents an indivisible traded contract for the bandwidth between two nodes.
  • a standard contract is for T3 (45 Mb/s) capacity with defined delay, jitter, packet loss, etc. and several time-scales of contracts are available with standardised starting times e.g. every 15 minutes, hours starting at :00, days starting at 00:00, and lengths. This degree of liquidity is not yet present or at least not yet widely observed for bandwidth trades but, considering how electricity markets developed, may be an eventual situation.
  • the nodes N are public pooling or inter-connection points where many carriers are present with the capability to arbitrarily cross-connect between networks. Thus, paths may be assembled in a supplier-neutral manner.
  • the bandwidth is offered for sale on the market in the form of point-to-point contracts that will generally comprise several underlying links L at the network- or physical layer.
  • the contract graph G(N,L) is an abstract view of network connectivity at the level of traded contracts, and links/paths in the contract graph G(N,L) do not map one-to-one to physical or network layer links or paths.
  • the contract graph abstraction is useful for studying the network effects inherent in a bandwidth market. That is, the price development on any link L is not independent of the prices of neighbouring links as there is generally more than one way to connect two locations and buyers will choose the cheapest path if the other factors are equal e.g. the QoS.
  • a Martingale referred to as M(t), is a stochastic process whose expected future value E is the same as its current value, i.e. for t s > t ⁇ ,
  • the primary traded commodities in the bandwidth telecom commodity market are futures contracts with fixed maturities and strike prices.
  • the prices of individual futures contracts over time are Martingales under the risk-neutral measure labelled Q and being equivalent to the real-world probability measure P, otherwise the futures market contains arbitrage opportunities.
  • the risk-neutral measure is a construct used in the pricing of derivative contracts. This observation is independent of whether the asset on which the forward is written is storable or non-storable because the forward contract itself is storable. Because bandwidth is non-storable, there is no reason to expect that the spot price p will be a Martingale under the risk-neutral measure. This does not mean that the market has arbitrage opportunities because the spot is not a tradable asset.
  • spot price process does not exist in the sense that the underlying asset can be bought at one time and sold at another time - which is usually the definition of tradable item.
  • a spot price process can be said to exist when it is possible to substitute the asset bought at one time for the asset bought at another time. For example a share of a stock bought today can be substituted for one bought tomorrow, and the buying person cannot distinguish between the two.
  • non-storability means that the spot commodity cannot be part of any self-financing strategy.
  • spot price process for the spot price p(T) is really just the set of forward prices F(T,T) at maturity. In this sense the spot price process does exist and is observable.
  • the forward prices F(T,T) at maturity, for any maturity 0 ⁇ T ⁇ *, are equivalent to the spot prices p(T), at that time - they are both the price p at the time T for delivery at the time T. It is assumed that the delivery of the forward assets is defined in the same way as the delivery of the spot assets.
  • F(T,T), O ⁇ T ⁇ T* need not be a Martingale because it is non-storable. For non-storable commodities the equivalence between F(T,T) and p(T) is complete.
  • F(0, T) p(0) e (r+u y> ⁇ , [26]
  • p(t) is the spot price at a time t
  • r is the (constant) interest rate
  • u are the storage costs, which are a fixed proportion of the spot price p
  • y is the convenience yield or fudge factor required to make both sides equal.
  • the fudge factor y is generally rationalised as the benefit from actually holding the commodity, e.g. the ability to benefit from temporary increases in the price p, also called shortages. A more sophisticated understanding of this term is to do with long- and short-term price dynamics. This relationship does not hold when the underlying asset is non-storable.
  • European futures options and derivatives Futures options are relatively simple to price and herein futures call options will be considered.
  • the payoff from a European futures call option is max(F(T,T)-X,Q) where X is the strike price, and F(T,T) ⁇ p(T) so also the payoff is equal to max(p(T)-X,0).
  • p(T) is not required to be a Martingale, although F(t,T) is with respect to t but not with respect to T. So in effect the futures call option can be treated as a call option on the spot.
  • the Black-Scholes option-pricing formula is not valid here because it assumes storability of the spot market asset. Equivalently the Black futures-option formula assumes log-normality of the futures price distribution, which in general, owing to the network effects, will also not be valid.
  • Equation [27] is a definition of, or at least a constraint on, the risk-neutral measure Q. Which of the two it is depends on other assumptions, especially the number of parameters in the stochastic process describing the forward price-development.
  • the e ⁇ term on both sides allows to compare present values when the present values are taken at time zero.
  • Equation [27] the forward contract F(0,T) is observed today, i.e. at time zero, on the market.
  • This forward contract F(0,T) is the amount to be paid at the time T, wherein the term e ⁇ rT converts this to the present value today.
  • the expected price of a call option on a futures contract E with the strike price X is defined by E Q ⁇ m F(T, T) - X, 0)) [28 ]
  • Equation [28] may be generalised to obtain the price p of any contingent claim C(0) that depends only on the distribution of the futures contract F(T,T), some set of deterministic parameters D and is European style i.e. is exercised only at T:
  • Fig. 10a shows the forwards curves for
  • DS3 capacity from New York to Los Angeles (NY-LA)
  • NY-LA New York to Los Angeles
  • Fig. 10b shows the forwards curves for DS3 capacity from New York to Los Angeles (NY-LA), with the delivery month starting in February 2001 and going to January 2002, and with a contract duration of one year at a monthly rate.
  • the dotted lines are buy quotes, the dashed lines depict sell quotes.
  • a constant interest rate was used for discounting the forward prices given in fig. 10 back to the present.
  • the used market-observed data were forward prices for December 2001, E(0,7), and for February 2001, which were used as p(0). Having no observations of forward volatility for December 2001, the value was set to 50% as a possible value. From fig. 10 it can be seen that forward prices are expected to halve on this timescale.
  • the risk-neutral probabilities Q were obtained indirectly by calibrating the Equations [23] and [24] according to Equation [27], i.e. the no-arbitrage condition, and to the given forward volatility. Given that there are four equations and two constraints, the risk-neutral measure is not unique. However, using the short-term volatility and the long-term trend as calibration parameters should be the least ambiguous choice. Whilst this fixes the first two moments of the distribution the higher moments are free and so is the shape of the distribution. The parameters for the networks (NY-CH-LA and NY-LA-SF) are different from those for the isolated link and so are the calculated distribution shape parameters.
  • Figure 11a shows the actual distributions of F(T,T) in the three different network situations (solid line) and without a network (light crossed line). Although the shape parameters may be different, the actual distributions appear very close to each other.
  • Fig. 1 lb shows the option price versus the strike price for a call option on forward price with and without a network, the strike and option prices being relative to F(0, T).
  • Q risk-neutral probability distribution
  • Figure 12 shows the percentage difference of the call option prices in the two network cases (solid line) from the isolated-link case (light crossed line). Up to a strike price of twice the forward price the difference in option values is less than 15%. Above this strike price it appears that there is numerical instability. Looking at Figure 1 la, b confirms this impression as the option values are becoming very low at these high strike prices so there is an instability due to division by small-numbers.
  • the reason may be that the forward is so far into the future that the accumulation of the no-geographical-arbitrage condition falls under the central limit theorem and results in a log-Normal-like distribution. If this is the case then the small differences seen in forward option prices at ten months may be much greater for shorter-dated options. It has hence been shown how to price European-style contingent claims on futures contracts of the same maturity. This involves calibrating the spot price process, which represents a non-storable commodity to the market-observed futures price, a Martingale under the risk-neutral measure Q.
  • the spot price process explicitly includes network effects, notably those from geographical arbitrage, and the markets' response to such conditions through load-balancing.
  • a typical combination of hardware and software could be a general purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.
  • the present invention can also be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein, and which - when loaded in a computer system - is able to carry out these methods.
  • Computer program means or computer program in the present context mean any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following a) conversion to another language, code or notation; b) reproduction in a different material form.

Abstract

L'invention concerne un procédé permettant de calculer, dans un réseau comportant des liaisons, le prix d'utilisation d'une liaison spécifique sur ledit réseau. Le procédé consiste à faire une comparaison (II) pour déterminer la différence de prix entre le prix d'utilisation de la liaison spécifique et celui d'un cheminement de rechange dans le réseau, qui ne comprend pas ladite liaison spécifique; à calculer le changement de prix (IV) pour déterminer un changement liaison-prix dans le prix d'utilisation de la liaison spécifique, et un changement liaison-prix dans le prix d'utilisation des liaisons du cheminement de rechange, en réponse à la différence de prix déterminée; à combiner (V), pour la liaison spécifique, les changements liaison-prix déterminés sur le prix d'utilisation de la liaison spécifique par rapport à toutes les liaisons sur le réseau, pour déterminer un changement de prix total pour la liaison spécifique; à fusionner (VII) le changement de prix total déterminé avec un changement de prix induit par le marché dans le prix d'utilisation de la liaison spécifique, pour calculer le prix d'utilisation de ladite liaison, le changement de prix induit par le marché étant entraîné par au moins une variable aléatoire.
PCT/IB2002/001187 2001-04-18 2002-04-02 Procede et dispositif de calcul du prix d'utilisation d'une liaison specifique d'un reseau WO2002085045A1 (fr)

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KR1020037013690A KR100634176B1 (ko) 2001-04-18 2002-04-02 네트워크의 특정 링크 사용 가격 계산 방법 및 장치
EP02718461A EP1380178B1 (fr) 2001-04-18 2002-04-02 Procede et dispositif de calcul du prix d'utilisation d'une liaison specifique d'un reseau
AT02718461T ATE480958T1 (de) 2001-04-18 2002-04-02 Verfahren und gerät zur berechnung eines preises für die verwendung einer spezifischen verbindung in einem netz
CA002443704A CA2443704A1 (fr) 2001-04-18 2002-04-02 Procede et dispositif de calcul du prix d'utilisation d'une liaison specifique d'un reseau
DE60237591T DE60237591D1 (de) 2001-04-18 2002-04-02 Verfahren und gerät zur berechnung eines preises für die verwendung einer spezifischen verbindung in einem netz
US10/475,185 US7742960B2 (en) 2001-04-18 2002-04-02 Method and device for calculating a price for using a specific link in a network
JP2002582640A JP2004538550A (ja) 2001-04-18 2002-04-02 ネットワーク内の特定のリンクを使用する価格を計算する方法および装置
AU2002249518A AU2002249518B2 (en) 2001-04-18 2002-04-02 Method and device for calculating a price for using a specific link in a network

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US6910024B2 (en) * 2000-02-04 2005-06-21 Hrl Laboratories, Llc System for pricing-based quality of service (PQoS) control in networks
US7742960B2 (en) * 2001-04-18 2010-06-22 International Business Machines Corporation Method and device for calculating a price for using a specific link in a network

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ATE480958T1 (de) 2010-09-15
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CA2443704A1 (fr) 2002-10-24
EP1380178B1 (fr) 2010-09-08
CN100568985C (zh) 2009-12-09
CN1505902A (zh) 2004-06-16
KR100634176B1 (ko) 2006-10-16
JP2004538550A (ja) 2004-12-24
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